Boltzmann Machines constitute a paramount class of neural networks for unsupervised learning and recommendation systems. Their bipartite version, called Restricted Boltzmann Machine (RBM), is the most developed because of its satisfactory trade-off between computability on classical computers and computational power. Though the diffusion of RBMs is quite limited as their training remains hard. Recently, a renewed interest has emerged as Adiabatic Quantum Computers (AQCs), which suggest a potential increase of the training speed with respect to conventional hardware. Due to the limited number of connections among the qubits forming the graph of existing hardware, associating one qubit per node of the neural network implies an incomplete graph. Thanks to embedding techniques, we developed a complete graph connecting nodes constituted by virtual qubits. The complete graph outperforms previous implementations based on incomplete graphs. Despite the fact that the learning rate per epoch is still slower with respect to a classical machine, the advantage is expected by the increase of number of nodes which impacts on the classical computational time but not on the quantum hardware based computation.

中文翻译：

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绝热量子计算机上的完全受限玻尔兹曼机

玻尔兹曼机器构成了用于无监督学习和推荐系统的一类最重要的神经网络。他们的二分版本，称为受限玻尔兹曼机 (RBM)，是最发达的，因为它在经典计算机的可计算性和计算能力之间取得了令人满意的平衡。尽管 RBM 的传播非常有限，因为它们的训练仍然很困难。最近，对绝热量子计算机 (AQC) 产生了新的兴趣，这表明相对于传统硬件可能会提高训练速度。由于构成现有硬件图形的量子比特之间的连接数量有限，因此神经网络的每个节点关联一个量子比特意味着一个不完整的图形。由于嵌入技术，我们开发了一个完整的图形连接由虚拟量子比特构成的节点。完整图优于以前基于不完整图的实现。尽管相对于经典机器，每个 epoch 的学习率仍然较慢，但可以通过增加节点数量来预期优势，这会影响经典计算时间，但不会影响基于量子硬件的计算。